Question: $A$ $B$ $C$ If: $ BC = 7x + 9$, $ AC = 70$, and $ AB = 6x + 9$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {6x + 9} + {7x + 9} = {70}$ Combine like terms: $ 13x + 18 = {70}$ Subtract $18$ from both sides: $ 13x = 52$ Divide both sides by $13$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $BC$ $ BC = 7({4}) + 9$ Simplify: $ {BC = 28 + 9}$ Simplify to find ${BC}$ : $ {BC = 37}$